A metallic rod of length `'L'` and cross-section `'A'` has Young's modulus `'Y'` and coefficient of linear expansion `'alpha'`. If the rod is heated to a temperature. 'T'` the energy stored per unit volume is:
A
`(Ya alphaLt^(2))/(2)`
B
`(Ya alpha^(2)Lt^(2))/(2)`
C
`(Ya alpha^(2)L^(2)t^(2))/(2)`
D
`(Ya alphaLt)/(2)`
Text Solution
Verified by Experts
The correct Answer is:
d
work perfomed by the rod `Delta` w= change in potential energy of the rod ` =1/2xx` stress x strian x volume `=1/2xxyxx("strains")^(2)x"AL"` `=1/2xxyxxalpha^(2) Delta t^(2)xxAL=(YA alpha^(2)Lt^(2))/(2) ["before" Delta L=L alpha t]`
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